Question

The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X:
What is the measure of angle ACB?
Select one:

a. 32°

b. 60°

c. 28°

d. 16°

Answer 1

Answer: A. 32°

Step-by-step explanation: how we find the measure of angle ACB is by taking the angle of arch BA and subtracting it by the angle of arch XA. then taking that number and dividing it by two.

so we know the angle of arch BA is 176° but we need to find arch XA. the angle of the arch XA is two times the measure of angle B

56 × 2 = 112

angle arch XA is 112°

now we plug both of those in for what i described earlier:

176 - 112 = 64

64 ÷ 2 = 32

angle ACB = 32°

hope this helped! :)